Answer
$(f+g)(-5)=44$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To evaluate the given expression, $
(f+g)(-5)
,$ given
\begin{array}{l}\require{cancel}
f(x)=x^2+3
\\
g(x)=-2x+6
,\end{array}
use the definition of the appropriate function operation. Then substitute $x$ with $
3
.$
$\bf{\text{Solution Details:}}$
Since $(f+g)(x)=f(x)+g(x),$ then
\begin{array}{l}\require{cancel}
(f+g)(x)=(x^2+3)+(-2x+6)
\\\\
(f+g)(x)=x^2+3-2x+6
\\\\
(f+g)(x)=x^2-2x+9
.\end{array}
Substituting $x$ with $
-5
,$ then
\begin{array}{l}\require{cancel}
(f+g)(-5)=(-5)^2-2(-5)+9
\\\\
(f+g)(-5)=25+10+9
\\\\
(f+g)(-5)=44
.\end{array}